A clicking noise may be noted from the turn signal flasher after the turn signals are switched off. This is commonly cause by a faulty turn signal switch which will require replacement.Google+
Car Problem Reports
Chevrolet Suburban 1500 Turn Signal Switch May Fail and Cause Clicking Noise
Chevrolet Suburban 1500 Problem
Average Mileage: 162,833 mi (120,000 mi - 196,000 mi)
Visitor, 1999 Chevrolet Suburban 1500, 152,000 mi
turn signal flasher is clicking no turn signal on, no brake lights, replaced flasher, no change
clicking comes and goes, dang..............
Visitor, 1999 Chevrolet Suburban 1500, 189,000 mi
Turn signal intermittently clicks as if it is engaged. Signals themselves appear to work normally however
Visitor, 2003 Chevrolet Suburban 1500, 130,000 mi
Mechanic said correction required pulling out entire dash / or under dash...Said not to worry about it...
Visitor, 1999 Chevrolet Suburban 1500, 190,000 mi
Turn signal sounds like it is on when it is off
Visitor, 1997 Chevrolet Suburban 1500, 120,000 mi
Clinking noise will occur even when blinker is not on.